Hop-congestion trade-offs for high-speed networks

Message transmission in ATM networks is via virtual paths. Packets are routed along virtual paths by maintaining a routing field whose subfields determine the intermediary destinations of the packet. In such a network it is important to construct path layouts that minimize the hop number (i.e. the number of virtual paths used to travel between any two nodes) as a function of edge-congestion (i.e. the number of virtual paths passing through a link). In this paper we construct asymptotically optimal virtual path layouts for chains and meshes